1) Discovery. Rdio would inform me when new albums are out by artists I listen to. Spotify doesn't. Rdio's "Artist Stations" were also much better – not only did they not repeat (like Spotify's do), they also let you choose whether you wanted to hear "more" or "less" of the artist themselves while listening to their station.
2) Social. I miss seeing my friends faces next to albums, letting me know that they'd listened to it. I also miss the "Network Heavy Rotation" view, that showed trending albums by friends/users I follow. I miss that a user's profile would show you what albums they've been listening to frequently lately. Spotify only tells you what track a friend is listening to right now, and their profile shows you what artists. So, awesome, you know your friend is listening to Bowie, but you don't know which of Bowie's 20 albums they're into.
3) Your collection. Rdio had no upper bound on saved albums (that I'm aware of). I've already peaked the maximum number of saved songs in Spotify – it literally won't let me "save" anything else without going through my existing albums and choosing something to remove.
4) Playlist searching. Spotify by default names your playlist according to the first song you've added. You have to go out of your way to give it a different name. This means there are TONS of playlists in Spotify that are named "Nirvana" purely because that was the first song in the playlist. It massively pollutes searching and makes finding good playlists tough. Also, there's no sensible ranking of playlists – Rdio would at least tell you which were the most popular, which was usually good enough.
There are about another dozen things I could name, but I'll stop here. Spotify has felt like a giant step backwards from Rdio, and I think I'm going to explore alternatives soon.